Minecraft broke

I can't get Minecraft working. It crashes every time I try to open a world. I have no idea what's happening to it but It seems like it maybe has something to do with Java?

I need to figure this out pretty soon, because I promised my nephew I'd play Minecraft with him this summer. He's like 7, and he remembered me promising well enough to ask me about it, so "I can't get it working" is not going to be a good enough answer.